Diesis

Referred DIESIS (Greek δίεσις " smallest interval " actually " pass" to diiēmi διΐημι " pass " )

  • In Italy and France increased chromatic naturals: The sound Fis is called in Italy "fa diesis ", in France "fa thèse ".
  • A small musical interval which occurs as small and large DIESIS in two forms.

Small DIESIS

If three major thirds strung together, so this result in equally- tempered tuning, one octave, in just intonation, however, a slightly smaller interval. The difference to the octave is called small DIESIS. Occasionally, the term enharmonic comma is used as the small DIESIS exactly makes up in just intonation and meantone tuning the difference between enharmonic change tones, for example, between Gis and As.

The pure major third has a frequency ratio of; three thirds those found thus

The octave with the frequency ratio is slightly larger. The two intervals differ by the interval ( an octave minus three major thirds ) with the frequency ratio:

(Note: 1 octave = 1200 cents. )

Large DIESIS

If four minor thirds strung together, so this result in equally- tempered tuning, one octave, in just intonation, however, a slightly larger interval. The difference to the octave is called large DIESIS.

The pure minor third has a frequency ratio of; four such thirds thus result.

The octave with the Frequemzverhältnis is slightly smaller; the difference is ( four minor thirds minus one octave):

History

Philolaos understands diesis the excess of the fourth above two whole tones ( Ditonus ), so the later than Limma designated diatonic semitone of the Pythagoreans. Aristoxenos used for the designation of all intervals that are smaller than a semitone. Marchetus de Padua defined in his Lucidarium the diesis than 1/5 whole tone.

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